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Up: Multi-period pulsation and amplitude Cephei

4 Discussion

Usually, the period analysis of the $\delta$ Scuti variables show a frequency near 1-2 cycle per day. This phenomenon is especially obvious in single-site observations and is probably due to the extinction and drift of the photometer. Therefore, we ignored the third frequency of 1.3488 cycle per day, as confirmation of its existence needs further observations.

The period analysis of DQ Cephei made by Pena (1983) for different years showed some evidences for amplitude variations. Combining all those results together, we listed the amplitudes of f1 and f2 in different years in Table 3 and plotted them in Fig. 3. We conclude that:

Amplitude variations of DQ Cephei are observable during a time scale of about a decade. If such variations are periodic, the period is longer than 46 years.
It seems that the amplitudes of the two pulsation modes vary in opposite phases, implying energy conservation.

If the amplitude variations are caused by the beat of two close frequencies, the split between these frequencies should be smaller than 0.0008 cycle per day, which is too small to be explained by a rotating split. If the split is caused by the overlap of different modes, DQ Cephei should be a high evolved $\delta$ Scuti. But this does not agree with the fact that DQ Cephei is a $\delta$ Scuti variable near the main sequence.

The calculation made by Moskalik (1985) shows that the time scale of amplitude modulation of $\delta$ Scuti caused by resonance coupling might reach several years. This does not support the opinion that the amplitude variation of DQ Cephei can be explained by the resonance coupling. Up to now, most $\delta$ Scuti show an amplitude variation with a time scale of about a decade, which is longer than those obtained with theoretical calculations.

\includegraphics [width=8.8cm]{}\end{figure} Figure 3: Amplitude variations of two modes

Table 3: The amplitude(magnitudes) variations of two frequencies in different years

 ...&0.024\\ $f_{2}=8.0480 $&0.0135&0.008&0.006&0.009\\  \hline

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